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In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the…

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…

Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…

Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…

Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides…

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…

Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

Topological Data Analysis (TDA) is increasingly crucial in investigating the shape of complex data structures across scientific fields, particularly in neuroscience and finance. This study delves into persistent homology, a TDA component…

Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an…

By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…

Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…

Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…

We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…

A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) and signal processing (e.g.,…

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "shape" of such complex high-dimensional data. Research in this…